Heartwarming / The Legend of Zelda: Phantom Hourglass
Ciela agreeing to help Link save Tetra because she's his friend and he wants to save her. She's pretty much agreeing to help a stranger on a dangerous journey out of pure altruism, despite the fact that she's struggling with her own amnesia. This is a stark contrast to Navi, who was only helping Link because the Great Deku Tree ordered her to do so, and Tatl helping Link out of her Big Sister Instinct to reunite with Tael before each had their own Character Development.
The special Item Get! from the first two dungeons. Normally, Link gets some sort of special item that is accompanied by a cinematic. In this case, Link meets two fairy companions, Leaf and Nari, who surround him as he laughs innocently at the thought of making a new friend. It's a reminder to the players that behind all the badass things that Link accomplished, he's still a child at heart.
Shortly after completing the third dungeon, Oshus reveals that the fairy that Link rescued is Ciela's missing half which contains her memories. He then reveals that he's the Ocean King, and uses his powers to fuse Ciela and her missing half together so that she can recover her memories and powers. Despite the shock of this sudden development, Ciela still sees Oshus as her adopted grandfather.
The best part of completing the first three dungeons is that all of the fairies act as an Equippable Ally, meaning that not only will they be able to help Link descend further into the Temple of the Ocean King, but also improve his fighting ability with their magic.
Returning to the Temple of the Ocean King for the third time will cause Link to receive a letter from Linebeck himself. Despite the letter's wording and content, it's clear that Linebeck started seeing Link as a friend, even if he has to express it by letter and he sounds like a Tsundere in the process. He even gives Link a Ship Part, which is quite generous given how cheap he is.
Saving Linebeck from Jolene and pirates causes him to give Link rewards. At first he gives Link small rupees, but each consecutive saving causes him to increase the reward until he pays him with Big Green Rupees, which are worth 100 rupees! Considering how much of a tightwad Linebeck is, it really says how grateful he is for Link's help.
One of the rewards he gives is a Courage Orb, which becomes important to Link when it is revealed that Ciela is the Spirit of Courage, and that her power had been divided into 20 Courage Orbs besides losing her memories. The fact that Linebeck actually helps Ciela recover her power despite how much they bicker, even if it is indirectly, is quite heartwarming.
They are brief, but every time Link gets mail from someone shows that deep down his efforts are much appreciated, especially if they come with a reward like a Ship Part or a Spirit Orb.
At least a day after completing a dungeon for each of the Pure Metals, Link will get a Spirit Orb from a character that benefitted from his visit to the islands on which the temples resided.
Salvatore sends him a Wisdom Orb for actually playing his bomb game regardless of the score Link gets.
Jolene being a Friendly Enemy to Link and asking him to send a letter to her little sister Joane, despite him getting in her way to get revenge on Linebeck. Joane then pays back Link with a letter expressing what a Cool Big Sis Jolene is and a Ship Part for Link to make up for his troubles.
The last fight with Jolene turns into this when she reveals that she knows about Link's exploits and how he intends to fight Bellum. She's not fighting him to get to Linebeck, she's fighting him because she does not want to see him get hurt, or worse, fighting against the Big Bad unless Link beats her.
To enter the Goron Temple, you have to be a member of the Goron Tribe. What does Link have to do to become an honorary member? Participate in a quiz! Link has to show how much he wants to be a member of the Gorons by paying a fine and then participating in a quiz about the Goron Tribe, which asks easy questions like "how many huts are there on the island?", or "how many Gorons live there?" as well. Though Link has to pay a fine if he misses any of the five questions, the Gorons reward him with increasing quantities of rupees for every consecutive answer he gets. Even if he fails and has to pay, Link is free to try the quiz as many times as he wants, showing that this incarnation of Gorons is the most social of the franchise.
Gongoron started as a Spoiled Brat who refused to help Link with the Goron Temple. However, after Link saved him from monsters, he underwent Character Development by helping Link navigate the temple and became Bash Brothers with him by temporarily defeating the dungeon boss, even feeling bad when the door was locked and Link had to defeat the monster on his own. The next time Link heard of him is through a letter containing a Courage Orb telling him that he got a job, showing that he started to mature.
Linebeck is pretty much this during the last part of the game. As Link and Ciela go to the Temple of the Ocean King to confront Bellum, Linebeck puts a Jerkass Fašade and pretends that he's only in it for the wish Oshus promised him in exchange for helping Link, and that he doesn't care if he's separated from Link and Ciela. However, it's obvious to everyone that he grew to care about the two, particularly when he tells Ciela to take care of Link. He later proved how much Link inspired him by helping him save Tetra from the Ghost Ship by personally navigating his ship while Link shoots the Ghost Ship, then fighting Bellum by using the Phantom Sword to defend Link when the latter was unconscious, despite ultimately getting himself possessed. Even his goodbye with Link and Ciela is this.
Linebeck using the wish Oshus gave him to restore the ship that was destroyed in the final battle with Bellum. It's a nice touch, considering the fact that Linebeck was shown to be very greedy and could have used the wish for material wealth. Additionally, the ending of the game implies (and future games later confirmed) that Linebeck later became a successful man on his own terms as a pirate and even a family man.
As divergent from the game as the manga of Phantom Hourglass was, they still did good with the scene where Linebeck is possessed by Bellum. He would rather kill himself than attack Link, and it's the only means of defiance he has.
At some point during the game, you get a letter in the mail from Linebeck. Seems strange at first since he's always travelling with Link, until the letter reveals that despite the way he usually acts, Linebeck really is grateful towards Link. He just finds it hard to actually say that to him.
When Link is forced to bid Ciela farewell, he reaches out to touch her one last time, and Ciela responds by gently resting herself in his hand. It's especially heartwarming, considering the last time he tried doing this to say goodbye to a companion.